On the Steinberg property of the Contou-Carrere symbol

Mathematics – Commutative Algebra

Scientific paper

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9 pages; a part on Witt parameters added; Lemma 3.2 modified

Scientific paper

The aim of this work is to show that the Contou-Carr\`{e}re symbol satisfies
the property of Steinberg symbols: $_{A((t))^\times} = 1$ for all
elements $f,1-f \in A((t))^\times$. Moreover, we offer a cohomological
characterization of the Contou-Carr\`{e}re symbol from the commutator of a
central extension of groups.

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